10. Five mark exercise problems II

1. The horizontal distance between two buildings is \(70 \ m\). The angle of depression of the top of the first building when seen from the top of the second building is \(45^{\circ}\). If the height of the second building is \(120 \ m\), find the height of the first building.

 

Answer:

 

The height of the first building is  .

 

(Note: Enter the number in the first box and the unit in the second box.)

 

2. From the top of the tower \(60 \ m\) high the angles of depression of the top and bottom of a vertical lamp post are observed to be \(38^{\circ}\) and \(60^{\circ}\) respectively. Find the height of the lamp post. (\(tan \ 38^{\circ} = 0.7813\), \(\sqrt{3} = 1.732\))

 

Answer:

 

The height of the lamp post is  .

 

(Note: Enter the number in the first box and the unit (short form) in the second box.)

 

3. An aeroplane at an altitude of \(1800 \ m\) finds that two boats are sailing towards it in the same direction. The angles of depression of the boats as observed from the aeroplane are \(60^{\circ}\) and \(30^{\circ}\) respectively. Find the distance between the two boats. (\(\sqrt{3} = 1.732\))

 

Answer:

 

The distance between the two boats is  .